Car A begins from rest at time t = 0, with constant acceleration a. Car B is mov
ID: 1705483 • Letter: C
Question
Car A begins from rest at time t = 0, with constant acceleration a. Car B is moving in the opposite direction at a constant speed v' = -V and, at t = 0, begins constant deceleration 1/3a. The
distance between the cars at t = 0 is d. When the cars pass each other, their speeds are equal.
(a) Determine the time at which the cars pass each other, t, their speed, |v(t)|, and the distance d. Express your answers in terms of V and a. Also, compute x(t)/d, where x(t) is distance from Car A’s initial position.
(b) If d = 200 m, V = 100 km/hr and the cars pass each other when t = 6 sec, compute a, |v(t)| and x(t).
Explanation / Answer
a) their speeds are equal when they passed each other. so we have. a*t = V - a*t. so t=V/2a so v(t)=a*t=V/2. x(t)=a*t^2/2=a*(V/2a)^2/2=V^2/8a. distance traveled by car B. x2(t)=V*t-at^2/2=V^2/2a-V^2/8a=0.375V^2/a. x(t)+x2(t)=d=0.5*V^2/a. so x(t)/d=1/4. b). a=V/2t=2.3(m/s2). v(t)=V/2=50(km/h). x(t)=V^2/8a=42(m).